How Fast Does a Ball Roll Down an Inclined Plane?

[sheri1987]

Homework Statement

A ball of mass 2.30 kg and radius 0.142 m is released from rest on a plane inclined at an angle q = 42.0° with respect to the horizontal. How fast is the ball moving (in m/s) after it has rolled a distance d=1.35 m? Assume that the ball rolls without slipping, and that its moment of inertia about its center of mass is 1.70E-2 kg·m2.

Homework Equations

.5mv^2+.5I(v^2/R^2) = mgdsin(angle)

The Attempt at a Solution

I plugged in the numbers to equation above and got 3.2 m/s by solving for v...am I doing something wrong, because it is not the right answer?!?

 

[Doc Al]

.5mv^2+.5I(v^2/R^2) = mgdsin(angle)

Your error is assuming that the only force acting on the ball parallel to the plane is the component of its weight. Not so. (What other force must act so that the ball rolls instead of slides?)

Edit: I was wrong--your equation is fine.

 

[nrqed]

Your error is assuming that the only force acting on the ball parallel to the plane is the component of its weight. Not so. (What other force must act so that the ball rolls instead of slides?)

I don't see the error in the OP's formula. The force you are thinking about does not do any work.

to the OP: What equation did you use for the moment of inertia? The one for a full sphere?

EDIT: never mind my last question, I had not noticed that the moment of inertia itself was given. Then it must simply be a mistake of plugging in the calculator.

 

[sheri1987]

I am not sure what other force, that is probably my problem

 

[Dick]

Your error is assuming that the only force acting on the ball parallel to the plane is the component of its weight. Not so. (What other force must act so that the ball rolls instead of slides?)

The OP is just using a conservation of energy equation. How can that be wrong? I put the numbers in and got a similar number but somewhat larger. I think it's just some kind of calculator slip up.

 

[Dick]

I don't see the error in the OP's formula. The force you are thinking about does not do any work.

to the OP: What equation did you use for the moment of inertia? The one for a full sphere?

It looks like the moment of inertia was given in the problem statement.

 

[Doc Al]

I don't see the error in the OP's formula. The force you are thinking about does not do any work.

You're right--my bad!

to the OP: What equation did you use for the moment of inertia? The one for a full sphere?

No equation needed--the moment of inertia is given.

The OP is just using a conservation of energy equation. How can that be wrong? I put the numbers in and got a similar number but somewhat larger. I think it's just some kind of calculator slip up.

Yep, you're right.

 

[nrqed]

It looks like the moment of inertia was given in the problem statement.

Yes, thank you. I edited my post when I noticed that.